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Numerical modeling of shallow non-Newtonian flows. I: The 1D horizontal dam break problem revisited. (English) Zbl 1302.35324
Summary: The dam break problem shallow approximation for laminar flows of power-law non-Newtonian fluids is numerically revisited under a time and space second order adaptive method. Theoretical solutions are compared with experimental measurements from the literature and new ones made of silicon. Asymptotic behaviours are solved numerically and from autosimilar solutions. The obtained theoretical results are finally compared with experiments. These comparisons confirm the validity of the shallow approximation equations for non-Newtonian fluids subject to the horizontal dam break problem.
MSC:
35Q35 PDEs in connection with fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76A05 Non-Newtonian fluids
76M10 Finite element methods applied to problems in fluid mechanics
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